Gee, in the book that Tolkien wrote, Gandalf tells Bilbo he has just ten minutes to get to the Green Dragon, and Bilbo runs the entire distance, "a mile or more", in just that time. I should think that any map drawn to match the text would either show the distance as about a mile, or be judged a bad map - whether it was drawn by Karen Fonstad or Tolkien himself.

Fonstad's map of the Shire in her Atlas simply copies and extends Tolkien's that appeared in Fellowship of the Ring, and her added scale (which Tolkien omitted) does seem to show the distance as five miles, relative to the distances the hobbits later cover to get to Buckland. But that does not mean the text in The Hobbit is wrong and that Gandalf magically sped Bilbo on his way! It's far more likely that Tolkien stretched the scale of his map at the center, to show both Hobbiton and Bywater more clearly; Fonstad herself cites the Hobbit text given above when she states that Bywater was just a mile from Hobbiton (or why would Hobbiton not have an Inn of its own?), without a word about the discrepancy this makes with her own map and Tolkien's.